Given a random variable $X$  normally distributed as $\operatorname{N}(m,\sigma^2)$ find probabilities $P(X \gt a),\; a \gt m;\;\;P(X \lt b),\;b \lt m$.

rebelmaths

Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.

Curl of a vector field.

Find modulus and argument of the complex number $z_1$ and find the $n$th roots of $z_1$ where $n=5,\;6$ or $7$.

5 questions on definite integrals - integrate polynomials, trig functions and exponentials; find the area under a graph; find volumes of revolution.

given equation of locus in form |z-a|=bfind centre and radius. multiple choice question

given random circle on graph with centre in 2nd or 3rd quadrant. find loci in complex form

Used for LANTITE preparation (Australia). NA = Number & Algebra strand. The total amount raised and the number of participants is supplied (and both are randomly generated). Students must calculate the average per participant. 

Used for LANTITE preparation (Australia). MG = Measurement & Geometry strand. The width and length of each vege bed are given in cm (randomised) as well as the path width in mm (randomised). Students are asked to find the perimeter of the whole vege patch in metres.

Just what the title says, I guess. I couldn't find a 0^0 that didn't converge to 1 except things like x^(1/ln(x)) as x->0, but they just need the e^ln() transformation, not L'hopital's rule!

Find the first 3 terms in the Taylor series at $x=c$ for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

Find the first 3 terms in the MacLaurin series for $f(x)=(a+bx)^{1/n}$ i.e. up to and including terms in $x^2$.

This exercise will help you rearrange a linear equation to find the value of a given variable

Attempt to apply Dijkstra's algorithm to find the shortest path from the source node (a) to a given sink node.

Apply the quadratic formula to find the roots of a given equation. The quadratic formula is given in the steps if the student requires it.

Using Pythagoras' theorem to determine a non-hypotenuse side, where side lengths include surds and students enter using sqrt syntax

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This exercise will help you rearrange a linear equation to find the value of a given variable

given trig function applied to tides. students need to find max depth, time of low tide and times between which a boat of given depth can use the port.

given trig equation. find period, amplitude and phase shift

given plot of a graph. find amplitude, period and phase shift

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Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Use a piecewise linear graph of speed against time to find the distance travelled by a car.

Finally, use the total distance travelled to find the average speed.

A 2D linear programming problem: optimise the profit from producing two different kinds of product, which both use the same limited resources.

A JSXGraph diagram illustrates the problem and can be used to find an answer.

Putting a pair of linear equations into matrix notation and then solving by finding the inverse of the coefficient matrix. 

In this assignment, try and find the roots of a randomly generated polynomial, using the quadratic equation.

A test assignment to see if it integrates properly into Canvas.

A simple question to find the roots of a quadratic. Using to test integration of NUmbas into Canvas.

Customised for the Numbas demo exam

Motion under gravity. Object is projected vertically with initial velocity $V\;m/s$. Find time to maximum height and the maximum height. Now includes an interactive plot.

This question provides a list of data to the student. They are asked to find the mean, median, mode and range.